The fourth dimension is, simply, something beyond our comprehension.
Or maybe, everything. As a mathematical possibility, the fourth
dimension begins with Euclid's Fifth Postulate, which outlines the following
proof:

According to this model, there are only three dimensions of linear direction:
variations of up, right, and forward. In other words, height, length, and
width. But even with all the practicality of Euclid's model, the concept
cannot be mathematically proven, opening the doorway to another fourth
direction. This is the possibility laid out by Einstein's Theory of
Relativity, which positions space as a curved, non-linear phenomenon. In
other words, there may be not only a fourth, but many 'directions'
we can't readily conceptualize.

That is the question. In many ways, it's in a direction we can't even
point to. Still, the possibilities and implications are so staggering that
the pursuit of the fourth dimension is not an endeavor to be dismissed.
Some have defined the elusive fourth direction as time, but even though
time is a direction of sorts, time is more of a function of the fourth
dimension as opposed to its definition. Because of the nature of a 'new
space', we may be able to see it only as a time-based phenomenon.

But even viewing the fourth dimension as time-based only gives us a limited
perspective. As Euclid's failed model shows, science can only go so far
to explore this undiscovered country -- there must be other ways to get
there.

As an unknown, unsignifiable quantity, the fourth dimension emerges
as not only an impetus for, but as an exercise and test for art. As ideas
about the fourth dimension begin to form in the early half of the century,
the parallel movements in Modernist art and literature cannot be consigned
to mutually-exclusive spaces. Within this context, Modernist art and literature
can be looked at for their own definitions of what this fourth dimension
might look like, signify, be.